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Phase slip and magnetoresistance of oxygen deficient YBa2Cu3O7−x
Physica C 235-240 (1994) 1977-1978
PHYICA
North-Holland
Phase slip and magnetoresistance of oxygen deficient YBa2Cu307_ x G. A. Kapustin a, H. A. Blackstead b, aRussian Research Centre "Kurchatov Institute", Moscow 123182, Russia. bDepartment of Physics, University of Notre Dame, Notre Dame IN46556, USA.
An application of the phase-slip model fer description of the resistive state in the oxygen deficient YBa2Cu3OT-x compound has been investigated. This model explains the energy dissipation in the mixed state of high-Tc layered superconductor by the mechanism of a phase slip resulting from the vortex movement through the network of intragrain intrinsic Josephson junctions. Good agreement has been achieved between the results of the calculation in terms of this model and the results of experimental measurements of the magnetoresistance for two samples with different critical temperatures, Tc = 58.8 K and 46.3 K (with x = 0.35; 0.46, accordingly) at high temperatures (0.6 < T/Tc < 1) and for magnetac field up to 40 T. For low temperatures (0.15 < T/Tc < 0.6) the experiment gives a sharper RiB) dependence.
At the present time there exist several models for the description of the resistive state of high-Tc superconductors (HTSCs), arising in the region of the magnetic moment reversibility and at the magnetic fields (including a "force-free" configuration B II j), which are essentially lower than the upper critical field Be2. One of these models proposed by M. Tinkham [1 1 a n d modified by H. Blackstead [21 and H. Blackstead and J. Philhps [3 ] h a s been successfully applied to the description of such state in a n u m b e r of HTSCs: 90 K -YBCO, Bi2212 and T12223. This model attributes t h e energy dissipation in the mixed state of layered HTSC to the phase slip mechanisn resulting from the vortex movement through the n e t w o r k of i n t r a g r a i n i n t r i n s i c Josephson junctions. Such junctions are formed between the fragments of the nearest Cu-O planes, separated from the neighboring fragments in the same plane by planar defects. In accordance with thas model the sample resistance can be expressed as function R -- Rn/Iio((7o/2) ~)
12
(1)
of one variable in the form of
70 = B0(1-t)n/B.
(2)
Here I0 is a modified Bessel function, Rn is the normal resistance, B0 is defined by the barrier height, t = T / T c , n = 3 / 2 - - c o n s t . An important
consequence of the modified model [2, 3 1 is the appearance of the power fl -- d / ( d + 2) in Eq. 1. This index is a distinctive feature of stretched exponential relaxatmn and is defined by the dimensionality ( d ) of the configuration space [3 I. Usually the resistive state is observed in a relattvely a a n o w region of temperatures (- 0 . i 5 ) a n o " m t~t g n "e l ]"~' - , l~l. C. l .U.5. . [. l.i p. . |. U 40 T) whach hes above the arreversabd~ty hne. The n value m Eq. 2 one can determine using a scahng relation B* c~ (1 - t*) n (here t* = T*/Tc) [4 ]. This relation interconnects the values of the magnetic field B* and temperature T*, meeting the condition k = R (B*, T*)/RniT*) = const (here Rn iT) as the normal resistance, extrapolated from T > Tc). In Fig. 2 a log-log plot of the B*(I - t*) d e p e n d e n c e as shown for v a r m u s k values.
0921-4534/94/S07 00 © 1994 - i.lsevmr Scmnce B V. All nghts reserved SSDI 0921-4534(94)01555-4
G.A Kapustm, H.A Blackstead/ Phy,~ca C 235-240 (1994) 1977-1978
1978
120 [
100
T,K 65 O
~100 l
~Qao ~
"'"'"""
. . . . ""
........
e, ~.6 6 L,a.L A ~ A
•
+0 I,+
II
6 6 n 6 n ~
•
~•i•
•
0ooo o•
"/ "/
o "" 01
o°•••¢o°°° &
10
~.
o- 0
64100¢
o
. . . . . . . . z•
"
o
IIJ
°
t
i
I
0
IO
20
I
30 B, T 40
Fig. I. Sample resistance (x = 0.35) vs. magnetic held. Solid curves repregent experimental data [4 ], points are calculated by the model [I-3 ]. S t r a i g h t h n e s a r e d r a w n t h r o u g h the points corresponding to the values of k = 0.3, 0.5, 0.8 m the temperature range 0.6 < t < 1. In thin range n = 1.43 _+ 0.03 (for x = 0.35), which is close to n -3/2 [1 ]. For x = 0.46 this value is significantly higher ( - - 2 ) a n d depends noticeably on k. At low temperatures the character of the interconnection between B* a n d t* changes. The B*(1 - t*) curves for different k values draw together with the t* decrease. This fact corresponds to relative narrowing of the normal state transition as the temperature lowers. It is very likely that at T -~ 0 these curves will meet at some point. This convergence corresponds to the sharp normal state transition. In Fig. 1 the experimental R(B, T) dependences a r e c o m p a r e d with the ones calculated from Eqs. 1 a n d 2 with n = 1.43, B• = 105 T and fl-- 1/2. For the calculahon a mgnihcant (~7 K) width of the resistwe transition at B = 0 was :aken mr• account. For this reason temperature To(k) for the given level k of the relatwe resistance at B = n ..... used as Tc m Eq. 2. The calculahon .snOWeO .... that at the high temperatures (0.6 < t < 1) the R(B, T) d e p e n d e n c e for 60 K-YBCO can be d. scribed well by Eqs. I and 2 with ~5= 1/2 1) This v
.
~
I) Shoulders on the R(B) dependences at k = 0 2 5 are, apparently, connecled wtth the breaking of wea~ hnks between crystallites by lhe rnagncttc field
00l
i
01
1--t*
I
Fig. 2. M a g n e t i c field B* vs. 1 - t* for t h e s a m p l e w i t h x = 0 . 3 5 ( p o i n t s ) . k: o - 0.3, @ - 0 . 4 , A - 0 . 5 , &, - 0 . 6 , :3 - 0 . 7 , • - 0 . 8 .
fl value corresponds to the 2-D configuration space and is intermediate between the values fl = 1 in relatively weakly ants•tropic 90 K-YBCO a n d fl = 1/3 in high-ants•tropic layered HTSCs Bi2212 and TI2223. At t < 0.6 an essential divergence is observed between the experimental curves a n d the calculated ones. More sharp experimental R(B) dependence is the evidence of the obligatory correction of the model [ 1-3 ] for low temperatures. ACKNOWLEDGEMENTS GAK gratefully acknowledges the Scientific Council on HTSC for partial support of this work in the framework of Project No. 93091 of the State Program of Russia, " H i g h - T e m p e r a t u r e Superc o n d u c t i v i t y " . HAB g r a t e f u l l y a c k n o w l e d g e s support from the M i d w e s t S u p e r c o n d u c t i n g Consortmm through US Department of Energy Grant DE-FG02 90ER45427. REFERENCES 1. M. T m k h a m , P h y s . Rev. Lett., 61 (1988) 1658. 2. H. A. Blackstead, Solid St. Comm., 87 ti993) 35. 3. H.A. Blackstead and J. C. Phllhps, to be pubhshed. 4. G. K a p u s t ~ n el al, P r o c e e d i n g s o f 7 t h International Workshop on Critical Currents m Superconductors, Alpbach, 1994, m print.
PHYICA
North-Holland
Phase slip and magnetoresistance of oxygen deficient YBa2Cu307_ x G. A. Kapustin a, H. A. Blackstead b, aRussian Research Centre "Kurchatov Institute", Moscow 123182, Russia. bDepartment of Physics, University of Notre Dame, Notre Dame IN46556, USA.
An application of the phase-slip model fer description of the resistive state in the oxygen deficient YBa2Cu3OT-x compound has been investigated. This model explains the energy dissipation in the mixed state of high-Tc layered superconductor by the mechanism of a phase slip resulting from the vortex movement through the network of intragrain intrinsic Josephson junctions. Good agreement has been achieved between the results of the calculation in terms of this model and the results of experimental measurements of the magnetoresistance for two samples with different critical temperatures, Tc = 58.8 K and 46.3 K (with x = 0.35; 0.46, accordingly) at high temperatures (0.6 < T/Tc < 1) and for magnetac field up to 40 T. For low temperatures (0.15 < T/Tc < 0.6) the experiment gives a sharper RiB) dependence.
At the present time there exist several models for the description of the resistive state of high-Tc superconductors (HTSCs), arising in the region of the magnetic moment reversibility and at the magnetic fields (including a "force-free" configuration B II j), which are essentially lower than the upper critical field Be2. One of these models proposed by M. Tinkham [1 1 a n d modified by H. Blackstead [21 and H. Blackstead and J. Philhps [3 ] h a s been successfully applied to the description of such state in a n u m b e r of HTSCs: 90 K -YBCO, Bi2212 and T12223. This model attributes t h e energy dissipation in the mixed state of layered HTSC to the phase slip mechanisn resulting from the vortex movement through the n e t w o r k of i n t r a g r a i n i n t r i n s i c Josephson junctions. Such junctions are formed between the fragments of the nearest Cu-O planes, separated from the neighboring fragments in the same plane by planar defects. In accordance with thas model the sample resistance can be expressed as function R -- Rn/Iio((7o/2) ~)
12
(1)
of one variable in the form of
70 = B0(1-t)n/B.
(2)
Here I0 is a modified Bessel function, Rn is the normal resistance, B0 is defined by the barrier height, t = T / T c , n = 3 / 2 - - c o n s t . An important
consequence of the modified model [2, 3 1 is the appearance of the power fl -- d / ( d + 2) in Eq. 1. This index is a distinctive feature of stretched exponential relaxatmn and is defined by the dimensionality ( d ) of the configuration space [3 I. Usually the resistive state is observed in a relattvely a a n o w region of temperatures (-
0921-4534/94/S07 00 © 1994 - i.lsevmr Scmnce B V. All nghts reserved SSDI 0921-4534(94)01555-4
G.A Kapustm, H.A Blackstead/ Phy,~ca C 235-240 (1994) 1977-1978
1978
120 [
100
T,K 65 O
~100 l
~Qao ~
"'"'"""
. . . . ""
........
e, ~.6 6 L,a.L A ~ A
•
+0 I,+
II
6 6 n 6 n ~
•
~•i•
•
0ooo o•
"/ "/
o "" 01
o°•••¢o°°° &
10
~.
o- 0
64100¢
o
. . . . . . . . z•
"
o
IIJ
°
t
i
I
0
IO
20
I
30 B, T 40
Fig. I. Sample resistance (x = 0.35) vs. magnetic held. Solid curves repregent experimental data [4 ], points are calculated by the model [I-3 ]. S t r a i g h t h n e s a r e d r a w n t h r o u g h the points corresponding to the values of k = 0.3, 0.5, 0.8 m the temperature range 0.6 < t < 1. In thin range n = 1.43 _+ 0.03 (for x = 0.35), which is close to n -3/2 [1 ]. For x = 0.46 this value is significantly higher ( - - 2 ) a n d depends noticeably on k. At low temperatures the character of the interconnection between B* a n d t* changes. The B*(1 - t*) curves for different k values draw together with the t* decrease. This fact corresponds to relative narrowing of the normal state transition as the temperature lowers. It is very likely that at T -~ 0 these curves will meet at some point. This convergence corresponds to the sharp normal state transition. In Fig. 1 the experimental R(B, T) dependences a r e c o m p a r e d with the ones calculated from Eqs. 1 a n d 2 with n = 1.43, B• = 105 T and fl-- 1/2. For the calculahon a mgnihcant (~7 K) width of the resistwe transition at B = 0 was :aken mr• account. For this reason temperature To(k) for the given level k of the relatwe resistance at B = n ..... used as Tc m Eq. 2. The calculahon .snOWeO .... that at the high temperatures (0.6 < t < 1) the R(B, T) d e p e n d e n c e for 60 K-YBCO can be d. scribed well by Eqs. I and 2 with ~5= 1/2 1) This v
.
~
I) Shoulders on the R(B) dependences at k = 0 2 5 are, apparently, connecled wtth the breaking of wea~ hnks between crystallites by lhe rnagncttc field
00l
i
01
1--t*
I
Fig. 2. M a g n e t i c field B* vs. 1 - t* for t h e s a m p l e w i t h x = 0 . 3 5 ( p o i n t s ) . k: o - 0.3, @ - 0 . 4 , A - 0 . 5 , &, - 0 . 6 , :3 - 0 . 7 , • - 0 . 8 .
fl value corresponds to the 2-D configuration space and is intermediate between the values fl = 1 in relatively weakly ants•tropic 90 K-YBCO a n d fl = 1/3 in high-ants•tropic layered HTSCs Bi2212 and TI2223. At t < 0.6 an essential divergence is observed between the experimental curves a n d the calculated ones. More sharp experimental R(B) dependence is the evidence of the obligatory correction of the model [ 1-3 ] for low temperatures. ACKNOWLEDGEMENTS GAK gratefully acknowledges the Scientific Council on HTSC for partial support of this work in the framework of Project No. 93091 of the State Program of Russia, " H i g h - T e m p e r a t u r e Superc o n d u c t i v i t y " . HAB g r a t e f u l l y a c k n o w l e d g e s support from the M i d w e s t S u p e r c o n d u c t i n g Consortmm through US Department of Energy Grant DE-FG02 90ER45427. REFERENCES 1. M. T m k h a m , P h y s . Rev. Lett., 61 (1988) 1658. 2. H. A. Blackstead, Solid St. Comm., 87 ti993) 35. 3. H.A. Blackstead and J. C. Phllhps, to be pubhshed. 4. G. K a p u s t ~ n el al, P r o c e e d i n g s o f 7 t h International Workshop on Critical Currents m Superconductors, Alpbach, 1994, m print.